TY - JOUR
T1 - On affine variety codes from the Klein quartic
AU - Geil, Hans Olav
AU - Ozbudak, Ferruh
PY - 2019/3/15
Y1 - 2019/3/15
N2 - We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in Kolluru et al., (Appl. Algebra Engrg. Comm. Comput. 10(6):433–464, 2000, Ex. 3.2). Among the codes that we construct almost all have parameters as good as the best known codes according to Grassl (2007) and in the remaining few cases the parameters are almost as good. To establish the code parameters we apply the footprint bound (Geil and Høholdt, IEEE Trans. Inform. Theory 46(2), 635–641, 2000 and Høholdt 1998) from Gröbner basis theory and for this purpose we develop a new method where we inspired by Buchberger’s algorithm perform a series of symbolic computations.
AB - We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in Kolluru et al., (Appl. Algebra Engrg. Comm. Comput. 10(6):433–464, 2000, Ex. 3.2). Among the codes that we construct almost all have parameters as good as the best known codes according to Grassl (2007) and in the remaining few cases the parameters are almost as good. To establish the code parameters we apply the footprint bound (Geil and Høholdt, IEEE Trans. Inform. Theory 46(2), 635–641, 2000 and Høholdt 1998) from Gröbner basis theory and for this purpose we develop a new method where we inspired by Buchberger’s algorithm perform a series of symbolic computations.
KW - Affine variety codes
KW - Gröbner basis
KW - Klein curve
UR - http://www.scopus.com/inward/record.url?scp=85063296125&partnerID=8YFLogxK
U2 - 10.1007/s12095-018-0285-6
DO - 10.1007/s12095-018-0285-6
M3 - Journal article
SN - 1936-2447
VL - 11
SP - 237
EP - 257
JO - Cryptography and Communications
JF - Cryptography and Communications
IS - 2
ER -